Bounds for the solution of hyperbolic problems

This article describes a newly developed and implemented method for computing guaranteed errorbounds for the solution of hyperbolic initial value problems. The basic concepts—modified fixed point theorems and approximated operators—allow an a posteriori error-estimation automatically. Therefore, no a priori knowledge of Lipschitz constants, monotonicity properties or additional error analysis is necessary.     

Completeness for nondeterministic complexity classes

We demonstrate differences between reducibilities and corresponding completeness notions for nondeterministic time and space classes. For time classes the studied completeness notions under polynomial-time bounded (even logarithmic-space bounded) reducibilities turn out to be different for any class containingNE. For space classes the completeness notions under logspace reducibilities can be separated for any class properly containingLOGSPACE. Key observation in obtaining the separations is the honesty property of reductions, which was recently observed to hold for the time classes and can be shown to hold for space classes.The work of S. Homer was supported in part by National Science Foundation Grants MIP-8608137 and CCR-8814339 and a Fulbright-Hays Research Fellowship. Some of this research was done while he was a Guest Professor at the Mathematics Institute of Heidelberg University.     

Motion patterns of Nabesna Glacier (Alaska) revealed by interferometric SAR techniques

Nabesna Glacier is one of the longest land-terminus mountain glaciers in North America. However, its flow has never been studied. We derived detailed motion patterns of Nabesna Glacier in winter and spring 1994–1996 from the synthetic aperture radar (SAR) images acquired by the European Remote Sensing satellites (ERS-1 and ERS-2) using interferometric SAR (InSAR) techniques. Special effort was made to assess the accuracy of the motion estimates, and remove data points with high uncertainty from the motion profiles, enabling us to obtain reliable glacier flow patterns along the highly curved main course of Nabesna Glacier. The results, covering 80 km of the 87 km main course of the glacier, were used to delineate four distinctive sections in terms of spatial and temporal variability of the glacier speed: (1) the upper section where glacier flow was apparently random both temporally and spatially presumably due to development of crevasses; (2) the upper-middle section with relatively steady flow around 0.27 to 0.4 m/day; (3) the middle section with a stable pattern of acceleration from 0.27–0.3 m/day to the maximum about 0.67–0.73 m/day, followed by a general deceleration to 0.17–0.33 m/day before reaching (4) the lower section where the glacier motion was generally slow yet highly variable although uncertainty in the estimation is high. Occurrence of the flow maximum, as well as many local maxima and minima at consistent locations over different periods suggests that the valley geometry affect the overall flow pattern. On top of this general trend, many small-scale temporal/spatial variations in the glacier flow patterns were observed along the glacier, especially in the lower sections. On average, the flow speeds were in the range of 0.3 to 0.7 m/day; however this lacks any measurements of summer flow speeds which are expected to be significantly higher.     

Biaxiale Ermüdung reibrührgeschweißter Strukturelemente

Biaxial fatigue of friction stir welded stiffened panels Within the framework of the European WelAir project, cruciform specimens made from stiffening FSW overlap joints were fatigued in the DLR biaxial test rig. To resemble the loading situation of pressurized fuselage structures, proportional loading without any phase shift, but with different load ratios λ between the loading components in both directions was applied.Natural crack initiation and subsequent crack growth were governed by the stiffness gradient caused by introducing the stringer. Cracks initiated and propagated at run‐in and run‐out locations in a direction perpendicular to the weld seam. The shortest fatigue life was observed for uniaxial loading in welding direction (λ = 0). An additional stress component perpendicular to the joint line (λ > 0) resulted in a higher number of cycles to failure. Similar to single stringer panels, increasing the load ratio also increased the number of cycles to failure for FSW clip‐stringer structural members, but additionally gives a different location of the fatal crack.     

Visual insights into high-resolution earthquake Simulations.

This study focuses on the visualization of a series of large earthquake simulations collectively called TeraShake. The simulation series aims to assess the impact of San Andreas Fault earthquake scenarios in Southern California. We discuss the role of visualization in gaining scientific insight and aiding unexpected discoveries.